PRECALCULUS Summer Math Packet

Transcription

1 PRECALCULUS Summer Math Packet In preparation for Pre-Calculus, we have prepared a packet of concepts that students should know how to do. These concepts have been taught in previous math classes. This packet does not require you to use a calculator; in fact you should not use a calculator at all on any of these problems. Pre-Calculus builds on the concepts in this packet. We start teaching Pre-Calculus concepts on the first day of school. We epect you to know the concepts in the packet in order to help you be successful in Pre-Calculus. If you are struggling with this packet, get help from a friend, parent, or tutor. If you can t find someone to help you, there are tutors available. A list of tutors can be found by calling Reagan High School. Keep in mind these tutors may charge a fee. You will have a graded assignment within the first two weeks of school. The graded assignment will cover all the concepts in the packet, but will not be the eact same problems. The graded assignment will be without a calculator. You can go to youtube and type in the name of the concept and watch math teachers eplain the concepts FOR FREE. DO THIS IF YOU FORGET HOW TO DO SOMETHING!!!!!!!! TABLE OF CONTENTS ) Multiplying Polynomials page (KEY p. ) ) Factoring page (KEY p. 6) ) Adding & Subtracting Fractions page (KEY p. ) ) Multiplying & Dividing Fractions page (KEY p. 8) ) Rationalize the Denominator page 6 (KEY p. 0) 6) Solve Quadratic Equations page (KEY p. ) ) Parent Function Graphs & Finding Domain page 8 (KEY p. ) 8) Rational Equations page 9 (KEY p. ) 9) Logarithms page 0 (KEY p. ) 0) Radical Equations page (KEY p. ) ) Absolute Value Equations page (KEY p. 8) ) ANSWER KEYS page

2 ) Multiplying Polynomials No Calculator!!!. ).. h. 6. h h 8. a b

3 ) Factoring No Calculator!! Factor each polynomial completely. If the polynomial cannot be factored write prime. ) 8 ) 0 ) a 6b ) 0 0 ) 6) 6 6 ) 8) 9) 6 8 0) c cd d ) y ) 0 ) 00 ) 6 ) a a 6) ) n n np p 8) 9 60

4 ) Adding & Subtracting Fractions No Calculator!!! Simplify each epression y

5 ) Multiplying & Dividing Fractions No Calculator!!! Simplify each epression

6 .. y z. Remember you cannot cancel at the beginning!!!. 6.

7 6 ) Rationalize the Denominator No Calculator!! ) ) ) ) 6 ) i i 6) 6 6 i i ) i i

8 Find all real and imaginary solutions for all problems. Solve the following by factoring. ) ) 6) Solve Quadratic Equations No Calculator!! 90 ) 8 ) 6 ) 6 8 Solve the following by using the square root property. 6) 0 ) 0 8) 9) 0 0) y 8 Solve the following by completing the square. ) 0 8 ) 0 ) Solve the following using the Quadratic Formula. You should have the Quadratic Formula memorized. ) 9 ) 6) 6

9 ) Parent Function Graphs & Finding Domain No Calculator!! PART : Be able to sketch the following parent function graphs: [ c implies any one constant number] y c, y, y, y, y, y, y a, y log, y, y sin, y cos PART : State the domain of each function using interval notation. See answer key for further eplanation if needed. ) f ) f f ) ) f 9 ) f 6) f ) f 8) f 0 8

10 8) Rational Equations No Calculator!!! Solve each rational equation. Remember the quadratic formula!!!

11 9) Logarithms No Calculator!!! Write each equation in logarithmic form.. 6. Write each equation in eponential form.. log 8. log 9 Evaluate each epression.. log log. log 8 8. log 6 9. log 8 Solve each equation. 0. log. log 8. log 6 0

12 . log. log log. log log 6. log 9 log 9 log 9. log log 8. log log

13 0) Radical Equations Solve each equation

14 ) Absolute Value Equations Solve each of the following equations. Remember to set up equations

15 ANSWER KEYS

16 ) Multiplying Polynomials ANSWERS No Calculator!!!. 9 ) h h h h. 6. h h 8 h h 8 8h. a b a ab b

17 ) Factoring ANSWERS No Calculator!! Factor each polynomial completely. If the polynomial cannot be factored write prime. ) 8 ) 0 ) a 6b a ba ab 6b ) 0 0 ) 6) (+8)(+8) ) 8) 9) ) c cd d ) y ) 0 c d c d y 9y y 9 ) 00 ) 6 ) a a 0 0 a a a a 6) ) n n np p 8) 9 60 n n p 6

18 Simplify each epression. ) Adding & Subtracting Fractions ANSWERS No Calculator!!! y. 6. 8y y

19 ) Multiplying & Dividing Fractions ANSWERS No Calculator!!! Simplify each epression

20 .. y z. y z Remember you cannot cancel at the beginning!!!. 6. 9

21 ) Rationalize the Denominator ANSWERS No Calculator!! ) 6 ) ) 6 ) 6 ) i i i 6) 6 i 6 6 i 9 9 i could write the answer all over 9 as one fraction ) i i i 0

22 Find all real and imaginary solutions for all problems. 6) Solve Quadratic Equations ANSWERS No Calculator!! Solve the following by factoring. ) ) 90 ) 8 X, X 9 0, 0 X, ) 6 ) 6 8 X 9, =, Solve the following by using the square root property. 6) 0 ) 0 8) X i 6 X X i 9) 0 0) y 8 6 X = 0, - Solve the following by completing the square. ) 0 8 ) 0 ) X 6 X i or i X i or 8 i Solve the following using the Quadratic Formula. You should have the Quadratic Formula memorized. ) 9 ) 6) i 9,

23 ) Parent Function Graphs & Finding Domain ANSWERS No Calculator!! PART : Be able to sketch the following parent function graphs: [ c implies any one constant number]

24 PART : State the domain of each function using interval notation. [Eclusions or restrictions of domain are results of problems in the equations when variables are replaced with numbers in various circumstances. For instance, square rooting a negative cannot be graphed on a real number plane because the answer is imaginary. Also, when a denominator equals 0, the answer is undefined and cannot be graphed on a real number plane. These problems result in numbers that must be ecluded from the domain. If no problems eist, there are no restrictions or eclusions and the domain is all real numbers written as.] (, ) ) f ) f ) f,,,, ) f 9 ) f 6) f,,,, ) f 8) f 0,,,,,66,

25 8) Rational Equations ANSWERS No Calculator!!! Solve each rational equation. Remember the quadratic formula!!!

26 9) Logarithms ANSWERS No Calculator!!! Write each equation in logarithmic form.. 6. log 6 log Write each equation in eponential form.. log 8. log Evaluate each epression.. log log. log 8-8. log 6 9. log 8 8 Solve each equation. 0. log. log 8. log 6 6

27 . log. log log - 6. log log 6. log 9 log log log log 8. log log 0 6

28 0) Radical Equations ANSWERS Solve each equation No solution /. 8 No solution

29 Solve each of the following equations. ) Absolute Value Equations ANSWERS. 6., -0, /, no solution. 6. No solution 8